Questions tagged [kerr-metric]

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Physical significance of angular velocity of orbits around Kerr black holes

For the Kerr metric $$ds^2=\left(g_{tt}-\frac{g_{t\phi}^2}{g_{\phi\phi}}\right)dt^2+g_{\phi\phi}\left(d\phi-\omega dt\right)^2+g_{rr}dr^2+g_{\theta\theta}d\theta^2$$ the angular momentum is defined as ...
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Gravitational lensing redshift around a Kerr black hole

Light from a source passes by a Kerr black hole on two sides at the equator and converges at the observer. The axis of rotation of the black hole is perpendicular to the direction of light. Two rays ...
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Beyond Kerr Carter constant?

What are the most symmetrical black hole spacetimes whose motion is completely integrable with a Carter constant-like and hidden symmetry superintegrability condition? Do type D-spacetimes have a ...
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Is a stable orbit possible inside the ergosphere of a Kerr (spinning) black hole?

I have heard that it's "impossible to hover" inside of an ergosphere, but everywhere I read this seemed to be speaking in the context of "relative to a stationary observer outside of the ergosphere". ...
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Visualization of $dtdx$ and $dxdy$ term in metric tensor

For the sake of simplicity, lets take a 2+1 dimensional spacetime. Lets take the metric $$ds^2 = g_{tt}dt^2 + g_{xx}dx^2 + g_{yy}dy^2 + g_{tx}dtdx + g_{xy}dxdy$$ What is the visualization or ...
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Centrifugal force on spinning black hole?

I saw the term spinning black hole popping up everywhere so my question do spinning black hole behave similarly to say a planet where it bulge in the equatorial and compress at the poles? what ...
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Kerr Black hole EH and Ergosphere embedding

Goodmorning everyone. I would like to share with you a question that has been gripping me for some time, but which I have never been able to give a convincing answer. When representing the ergosphere ...
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What would happen to the Earth, if the moon was a black hole? [closed]

Would it be a feasible scenario? I have read this question: What would happen to the Moon if Earth is turned into a black hole? Where Lubos Motl says: The extremal Kerr J=GM2/c∼RbhMc. Now, the ...
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Periodicity trick for Kerr Black Holes

I am slightly confused concerning the euclidean section of a Kerr black hole. In page 5 of the following paper https://arxiv.org/abs/hep-th/9908022 it is said that in order to get the euclidean ...
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Proof that the Kerr metric may be written in orthogonal form

Prove or disprove that the Kerr metric can be expressed in a set of orthogonal coordinates over some coordinate chart. Motivation for this question stems from my understanding that a metric can ...
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Kerr metric in BMS (Bondi-Metzner-Sachs) coordinates

I am trying to put the Kerr metric into the famous Bondi gauge, which is given for instance by the formula (6.2.10) at page 154 of the following paper: https://arxiv.org/abs/1801.01714. Now, Barnich ...
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Would naked singularities have a complex irreducible mass?

The formula for the irreducible mass, also known as the Christodoulou and Ruffini equation, is $$M_{\rm irr} = \frac{\sqrt{2 M^2-Q^2+2 M \sqrt{M^2-Q^2-a^2}}}{2}$$ where M is the mass equivalent of ...
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Kerr BH effects on inspiral binaries

In the gravitational wave calculation for binary systems: what is the effect of rotation of two BH (or neutron stars, BH-NS,...) on the usual calculations? Is there any EXACT result known?
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Calculate Komar mass and Komar angular momentum for the Kerr metric [closed]

I have this questions for HW: calculate Komar mass and Komar angular momentum for the Kerr metric. the quations that I see in the lecture notes are: in the notes it dosent explain the parameters ...
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Moment of inertia of a rotating black hole [duplicate]

The moment of inertia of a massive object about a given axis describes how its mass is distributed about that axis. I understand that a rotating black hole of a given mass and angular velocity ...
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Can rotating black hole have toroidal event horizon with penetrating relativistic jet(s)?

It is conjectured that a rotating black hole has at its center a ring-shaped singularity. Thus, at the center of the ring-shaped singularity the gravitational field must be zero (similar to ...
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If a black hole is made by a hypothetical particle above Planck mass and it has angular momentum will it be a ring Kerr black hole? [duplicate]

If a single subatomic hypothetical fundamental particle incapable of decay (such as an electron) with a mass exceeding Planck mass possessed angular momentum and it collapsed into a black hole, would ...
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de-Sitter spacetimes

In classical textbooks for GR, Schwarzschild and Kerr spacetimes are adequately described. In which books or articles, it is mostly believed that Reissner-Nordstrom, Kerr-Newman, Schwarzschild-de ...
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How to get the black hole spin in RPM if you have the value of $a$?

Most research papers use the variable "a" to describe black hole spin, which always has a value of less than 1, I don't know what this variable is called, but from what I know it can't exceed 1 ...
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Conservation equation of a perfect fluid in Kerr geometry

I am reading a paper in which a perfect fluid in the Kerr geometry is studied. The stress-energy tensor is \begin{equation} T_{\mu \nu} = (\epsilon + P) u_\mu u_\nu + P g_{\mu \nu}, \end{equation} ...
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Gram-Schmidt Orthonormalization

In the paper from Kulkarni et al., 2011 (Appendix B1), a method is given for transforming from Boyer-Lindquist (BL) coordinates to a comoving frame. This involves using Gram-Schmidt ...